A285106 a(n) = A001222(A284576(n)).

1, 2, 2, 3, 4, 5, 3, 4, 5, 7, 7, 6, 7, 8, 4, 5, 6, 8, 8, 9, 10, 10, 8, 8, 8, 10, 10, 9, 10, 11, 5, 6, 7, 9, 11, 10, 14, 16, 14, 13, 14, 13, 15, 17, 14, 16, 10, 10, 10, 11, 15, 14, 15, 17, 15, 13, 11, 13, 13, 12, 13, 14, 6, 7, 8, 10, 14, 13, 15, 19, 21, 17, 18, 20, 24, 25, 22, 20, 20, 16, 17, 19, 25, 23, 25, 30, 20, 22, 20, 20, 26, 26

Offset: 0

Author

Antti Karttunen, Apr 11 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A001222, A003986, A007306, A284576, A285107, A285108.

Programs

Scheme

(define (A285106 n) (A001222 (A284576 n)))
;; A more practical version, needing only an implementation of A003986bi (bitwise-or, A003986) and memoization-macro definec:
(define (A285106 n) (apply + (bitwise_or_of_exp_lists (A260443as_coeff_list n) (A260443as_coeff_list (+ 1 n)))))
(define (bitwise_or_of_exp_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (bitwise_or_of_exp_lists nums2 nums1)) (else (map A003986bi nums1 (append nums2 (make-list (- len1 len2) 0)))))))
(definec (A260443as_coeff_list n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_coeff_list (/ n 2)))) (else (add_two_lists (A260443as_coeff_list (/ (- n 1) 2)) (A260443as_coeff_list (/ (+ n 1) 2))))))
(define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))

Formula

a(n) = A001222(A284576(n)).

a(n) = A285107(n) + A285108(n).

Other identities. For all n >= 0:

A007306(1+n) = a(n) + A285108(n).